The results obtained are consistent with those found by [1]} which show that the qualitative response of the disc is same when the fluctuations are introduced in the \(\alpha \)  or directly to the viscosity which implies that perhaps they do not depend on the details of the viscosity prescription. The empirical functions obtained here, especially the dependence of the time-lag on frequency, will have utility in making models that predict the power spectra and time-lags of X-ray binaries within the framework of propagating fluctuations such as those described in [2]}, [3]}. In particular, the dampening of the fluctuation can be expressed using the empirical relation above and the time-lag between the accretion rate variation can be taken to be time-period (or frequency) dependent. These will no doubt have an impact on both the qualitative and quantitative interpretations that such models make.
